AS/A2 Pure 4 Pure 6

P5 Summary
The formulae
Check you know the definitions of the six hyperbolic trig functions.

The definitions in terms of exponentials
sinh x		cosh x
The other hyperbolic functions
tanh x		sech x
cosech x		coth x

The formula book available in the examination contains a large number of useful formulas for P5. Remember, you also need to be familiar with the formulae in P4 too, and those that need to be memorised from P1, P2 and P3. Coordinate systems
	Ellipse	Parabola	Hyperbola	Rectangular hyperbola
Standard form
Parametric form
Eccentricity	e<1	e=1	e>1	e=Ö2
Foci	(±ae,0)	(a,0)	(±ae,0)	(±Ö2c,±Ö2c)
Directrices		x=-a		x+y=±Ö2c
Asymptotes	none	none		x=0, y=0

Radius of curvature
Curvature
Radius of curvature

Hyperbolic functions

Differentiation
f(x)		f'(x)	f(x)	f'(x)
arcsin x			sinh x	cosh x
arccos x			cosh x	sinh x
arctan x			tanh x	sech2x
arcsinh x
arccosh x
arctanh x

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